Multiple equilibria in thermosolutal convection due to salt-flux boundary conditions

Long-term variability in the ocean's thermohaline circulation has attracted considerable attention recently in the context of past and future climate change. Drastic circulation changes are documented in paleoceanographic data and have been simulated by general circulation models of the ocean. The mechanism of spontaneous, abrupt changes in thermohaline circulation is studied here in an idealized context, using a two-dimensional Boussinesq fluid in a rectangular container, over 5 decades of Rayleigh number. When such a fluid is forced with a specified distribution of temperature and salinity at the surface — symmetric about a vertical axis - it attains a stable two-cell circulation, with the same symmetry. On the other hand, replacement of the specified salinity surface condition with an appropriate symmetric salt-flux condition leads to loss of stability of the symmetric circulation and gives rise to a new, asymmetric state. The extent of asymmetry depends on the magnitude of the thermal Rayleigh number, Ra, and on the strength of the salinity flux, γ. An approximate stability curve in the γ-Ra space, dividing the symmetric from the asymmetric states, is obtained numerically, and the entire range of asymmetric flows, from very slight dominance of one cell to its complete annihilation of the other cell, is explored. The physical mechanism of the pitchfork bifurcation from symmetric to asymmetric states is outlined. The effects of three other parameters of the problem are also discussed, along with implications of our results for glaciation cycles of the geological past and for interdecadal oscillations of the present ocean-atmosphere system.